The Fabric of Reality: The Science of Parallel Universes--and Its Implications

by David Deutsch

Thus, in a broad enough sense, taking into account the processes that must take place inside the scientist’s mind, science and the virtual-reality rendering of physically possible environments are two terms denoting the same activity.

Scientists’ thinking is virtual reality rendering; it is using the mind to conceive of possible experiences—experiences in the form of experiments, then tested in reality. Where virtual is incomplete, experiments reveal.

We might choose to render an environment as predicted by some ‘laws of physics’ that are different from the true laws of physics. We may do this as an exercise, or for fun, or as an approximation because the true rendering is too difficult or expensive. If the laws we are using are as close as we can make them to real ones, given the constraints under which we are operating, we may call these renderings ‘applied mathematics’ or ‘computing’. If the rendered objects are very different from physically possible ones, we may call the rendering ‘pure mathematics’. If a physically impossible environment is rendered for fun, we call it a ‘video game’ or ‘computer art’. All these are interpretations. They may be useful interpretations, or even essential in explaining our motives in composing a particular rendering. But as far as the rendering itself goes there is always an alternative interpretation, namely that it accurately depicts some physically possible environment.

What we experience directly is a virtual-reality rendering, conveniently generated for us by our unconscious minds from sensory data plus complex inborn and acquired theories (i.e. programs) about how to interpret them.

The ecological niche that human beings occupy depends on virtual reality as directly and as absolutely as the ecological niche that koala bears occupy depends on eucalyptus leaves.

Interpretation, of sensory information, being the part that makes us unique. We have explanations for the way the world is and could be. Only us.

virtual reality Any situation in which the user is given the experience of being in a specified environment.

The fact that virtual reality is possible is an important fact about the fabric of reality. It is the basis not only of computation, but of human imagination and external experience, science and mathematics, art and fiction.

The Turing principle It is possible to build a virtual-reality generator whose repertoire includes every physically possible environment.

This is the strongest form of the Turing principle. It not only tells us that various parts of reality can resemble one another. It tells us that a single physical object, buildable once and for all (apart from maintenance and a supply of additional memory when needed), can perform with unlimited accuracy the task of describing or mimicking any other part of the multiverse. The set of all behaviours and responses of that one object exactly mirrors the set of all behaviours and responses of all other physically possible objects and processes.

Thus, the laws of physics may be said to mandate their own comprehensibility.

The first thing to stress is that we do have only virtual reality based on the wrong laws to learn from! As I have said, all our external experiences are of virtual reality, generated by our own brains. And since our concepts and theories (whether inborn or learned) are never perfect, all our renderings are indeed inaccurate. That is to say, they give us the experience of an environment that is significantly different from the environment that we are really in. Mirages and other optical illusions are examples of this. Another is that we experience the Earth to be at rest beneath our feet, despite its rapid and complex motion in reality. Another is that we experience a single universe, and a single instance of our own conscious selves at a time, while in reality there are many. But these inaccurate and misleading experiences provide no argument against scientific reasoning. On the contrary, such deficiencies are its very starting-point.

However, there is a question we can still ask. Suppose that someone were imprisoned in a small, unrepresentative portion of our own reality — for instance, inside a universal virtual-reality generator that was programmed with the wrong laws of physics. What could such prisoners learn about our external reality? At first sight, it seems impossible that they could discover anything at all about it. It may seem that the most they could discover would be the laws of operation, i.e. the program, of the computer that operated their prison. But that is not so! Again, we must bear in mind that if the prisoners are scientists, they will be seeking explanations as well as predictions. In other words, they will not be content with merely knowing the program that operates their prison: they will want to explain the origin and attributes of the various entities, including themselves, that they observe in the reality they inhabit. But in most virtual-reality environments no such explanation exists, for the rendered objects do not originate there but have been designed in the external reality.

So even if you had lived within the rendered environment all your life, and did not have your own memories of the outside world to account for as well, your knowledge would not be confined to that environment. You would know that, even though the universe seemed to have a certain layout and obey certain laws, there must be a wider universe outside it, obeying different laws of physics. And you could even guess some of the ways in which these wider laws would have to differ

Anything that seems incomprehensible is regarded by science merely as evidence that there is something we have not yet understood, be it a conjuring trick, advanced technology or a new law of physics.

The rendered environment would also have to be such that no explanations of anything inside would ever require one to postulate an outside. The environment, in other words, would have to be self-contained as regards explanations. But I doubt that any part of reality, short of the whole thing, has that property.

The diagonal argument shows that the overwhelming majority of logically possible environments cannot be rendered in virtual reality. I have called them Cantgotu environments. There is nevertheless a comprehensive self-similarity in physical reality that is expressed in the Turing principle: it is possible to build a virtual-reality generator whose repertoire includes every physically possible environment. So a single, buildable physical object can mimic all the behaviours and responses of any other physically possible object or process. This is what makes reality comprehensible.

this book is not primarily a defence of the fundamental theories of the four main strands; it is an investigation of what those theories say, and what sort of reality they describe.

Justification based on merit of the ideas, not as foundational. In the event they are better theories for explaining and understanding reality, then that is sufficient justification in itself, regardless of arguments for or against other theories.

Science seeks better explanations. A scientific explanation accounts for our observations by postulating something about what reality is like and how it works. We deem an explanation to be better if it leaves fewer loose ends (such as entities whose properties are themselves unexplained), requires fewer and simpler postulates, is more general, meshes more easily with good explanations in other fields and so on. But why should a better explanation be what we always assume it to be in practice, namely the token of a truer theory? Why, for that matter, should a downright bad explanation (one that has none of the above attributes, say) necessarily be false? There is indeed no logically necessary connection between truth and explanatory power.

Well, Popperians might speak of a theory being the best available for use in practice, given a certain problem-situation. And the most important features of a problem-situation are: what theories and explanations are in contention, what arguments have been advanced, and what theories have been refuted. ‘Corroboration’ is not just the confirmation of the winning theory. It requires the experimental refutation of rival theories. Confirming instances in themselves have no significance.

In the Popperian picture of scientific progress, it is not observations but problems, controversies, theories and criticism that are primary. Experiments are designed and performed only to resolve controversies. Therefore only experimental results that actually do refute a theory — and not just any theory, it must have been a genuine contender in a rational controversy — constitute ‘corroboration’. And so it is only those experiments that provide evidence for the reliability of the winning theory.

the ‘reliability’ that corroboration confers is not absolute but only relative to the other contending theories. That is, we expect the strategy of relying on corroborated theories to select the best theories from those that are proposed. That is a sufficient basis for action. We do not need (and could not validly get) any assurance about how good even the best proposed course of action will be. Furthermore, we may always be mistaken, but so what? We cannot use theories that have yet to be proposed; nor can we correct errors that we cannot yet see.

Argument is not the same species of thing as deduction, or the non-existent induction. It is not based on anything or justified by anything. And it doesn’t have to be, because its purpose is to solve problems — to show that a given problem is solved by a given explanation.

A ‘deeper’ understanding is one that has more generality, incorporates more connections between superficially diverse truths, explains more with fewer unexplained assumptions. The most fundamental phenomena are implicated in the explanation of many other phenomena, but are themselves explained only by basic laws and principles.

By analogy with an ecological ‘niche’ (the set of environments in which an organism can survive and reproduce), I shall also use the term niche for the set of all possible environments which a given replicator would cause to make copies of it.

Idea-niche fit; the best niche is the one that promotes spontaneous or catalyzed replication of the idea by the environment and is hard the vary such that changing the idea even slightly kills its replication in that niche

If most variants of the replicator fail to cause most environments of its niche to copy them, then it would follow that our replicator’s form is a significant cause of its own copying in that niche, which is what we mean by saying that it is highly adapted to the niche. On the other hand, if most variants of the replicator would be copied in most of the environments of the niche, then the form of our replicator makes little difference, in that copying would occur anyway. In that case, our replicator makes little causal contribution to its copying, and it is not highly adapted to that niche. So the degree of adaptation of a replicator depends not only on what that replicator does in its actual environment, but also on what a vast number of other objects, most of which do not exist, would do, in a vast number of environments other than the actual one. We have encountered this curious sort of property before. The accuracy of a virtual-reality rendering depends not only on the responses the machine actually makes to what the user actually does, but also on responses it does not, in the event, make to things the user does not in fact do. This similarity between living processes and virtual reality is no coincidence,

An organism is not a replicator: it is part of the environment of replicators — usually the most important part after the other genes. The remainder of the environment is the type of habitat that can be occupied by the organism (such as mountain tops or ocean bottoms) and the particular life-style within that habitat (such as hunter or filter-feeder) which enables the organism to survive for long enough for its genes to be replicated.

Organisms are not copied during reproduction; far less do they cause their own copying. They are constructed afresh according to blueprints embodied in the parent organisms’ DNA.

This gene-based understanding of life — regarding organisms as part of the environment of genes — has implicitly been the basis of biology since Darwin, but it was overlooked until at least the 1960s, and not fully understood until Richard Dawkins published The Selfish Gene (1976) and The Extended Phenotype (1982).

But remarkably, this appearance is misleading. It is simply not true that life is insignificant in its physical effects, nor is it theoretically derivative. As a first step to explaining this, let me explain my earlier remark that life is a form of virtual-reality generation.

they exert exquisitely accurate, interactive control over the responses of a complex environment (the organism) to everything that may happen to it. And this control is directed towards causing the environment to act back upon the genes in a specific way (namely, to replicate them) such that the net effect on the genes is as independent as possible of what may be happening outside. This is more than just computing. It is virtual-reality rendering.

We can infer the ‘intention’ of genes to render an environment that will replicate them, from Darwin’s theory of evolution. Genes become extinct if they do not enact that ‘intention’ as efficiently or resolutely as other competing genes. So living processes and virtual-reality renderings are, superficial differences aside, the same sort of process. Both involve the physical embodying of general theories about an environment. In both cases these theories are used to realize that environment and to control, interactively, not just its instantaneous appearance but also its detailed response to general stimuli. Genes embody knowledge about their niches. Everything of fundamental significance about the phenomenon of life depends on this property, and not on replication per se.

It is the survival of knowledge, and not necessarily of the gene or any other physical object, that is the common factor between replicating and non-replicating genes. So, strictly speaking, it is a piece of knowledge rather than a physical object that is or is not adapted to a certain niche. If it is adapted, then it has the property that once it is embodied in that niche, it will tend to remain so.

The point is that although all known life is based on replicators, what the phenomenon of life is really about is knowledge. We can give a definition of adaptation directly in terms of knowledge: an entity is adapted to its niche if it embodies knowledge that causes the niche to keep that knowledge in existence. Now we are getting closer to the reason why life is fundamental. Life is about the physical embodiment of knowledge, and in Chapter 6 we came across a law of physics, the Turing principle, which is also about the physical embodiment of knowledge.

There is no getting away from it: the future history of the universe depends on the future history of knowledge. Astrologers used to believe that cosmic events influence human affairs; science believed for centuries that neither influences the other. Now we see that human affairs influence cosmic events.

Life achieves its effects not by being larger, more massive or more energetic than other physical processes, but by being more knowledgeable. In terms of its gross effect on the outcomes of physical processes, knowledge is at least as significant as any other physical quantity.

We can see that the ancient idea that living matter has special physical properties was almost true: it is not living matter but knowledge-bearing matter that is physically special. Within one universe it looks irregular; across universes it has a regular structure, like a crystal in the multiverse. So knowledge is a fundamental physical quantity after all, and the phenomenon of life is only slightly less so.

Where there is knowledge, there must have been life, at least in the past.

replicator An entity that causes certain environments to make copies of it.

niche The niche of a replicator is the set of all possible environments in which the replicator would cause its own replication. The niche of an organism is the set of all possible environments and life-styles in which it could live and reproduce.

adaptation The degree to which a replicator is adapted to a niche is the degree to which it causes its own replication in that niche. More generally, an entity is adapted to its niche to the extent that it embodies knowledge that causes the niche to keep that knowledge in existence.

life is associated with a fundamental principle of physics — the Turing principle — since it is the means by which virtual reality was first realized in nature. Also, despite appearances, life is a significant process on the largest scales of both time and space. The future behaviour of life will determine the future behaviour of stars and galaxies. And the largest-scale regular structure across universes exists where knowledge-bearing matter, such as brains or DNA gene segments, has evolved.

Quantum computation is more than just a faster, more miniaturized technology for implementing Turing machines. A quantum computer is a machine that uses uniquely quantum-mechanical effects, especially interference, to perform wholly new types of computation that would be impossible, even in principle, on any Turing machine and hence on any classical computer. Quantum computation is therefore nothing less than a distinctively new way of harnessing nature.

Quantum computation, which is now in its early infancy, is a distinct further step in this progression. It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes. A quantum computer would be capable of distributing components of a complex task among vast numbers of parallel universes, and then sharing the results.

So, the laws of physics not only permit (or, as I have argued, require) the existence of life and thought, they require them to be, in some appropriate sense, efficient. To express this crucial property of reality, modern analyses of universality usually postulate computers that are universal in an even stronger sense than the Turing principle would, on the face of it, require: not only are universal virtual-reality generators possible, it is possible to build them so that they do not require impracticably large resources to render simple aspects of reality. From now on, when I refer to universality I shall mean it in this sense, unless otherwise stated.

Anything that is calculable is calculable in a finite time. The laws of physics—the nature of reality—are efficient. What matters is what is or isn’t calculable.

Complexity theory has not yet been sufficiently well integrated with physics to give many quantitative answers. However, it has made a fair amount of headway in defining a useful, rough-and-ready distinction between tractable and intractable computational tasks.

What’s complexity theory?

What counts for ‘tractability’, according to the standard definitions, is not the actual time taken to multiply a particular pair of numbers, but the fact that the time does not increase too sharply when we apply the same method to ever larger numbers.

Tractability—whether a calculation can be calculated—is a matter of the rate of growth of the time required to run increasingly complex calculations on the same algorithm.

In 1982 the physicist Richard Feynman considered the computer simulation of quantum-mechanical objects. His starting-point was something that had already been known for some time without its significance being appreciated, namely that predicting the behaviour of quantum-mechanical systems (or, as we can describe it, rendering quantum-mechanical environments in virtual reality) is in general an intractable task.

In quantum mechanics, small deviations from a specified initial state tend to cause only small deviations from the predicted final state. Instead, accurate prediction is made difficult by quite a different effect. The laws of quantum mechanics require an object that is initially at a given position (in all universes) to ‘spread out’ in the multiverse sense. For instance, a photon and its other-universe counterparts all start from the same point on a glowing filament, but then move in trillions of different directions. When we later make a measurement of what has happened, we too become differentiated as each copy of us sees what has happened in our particular universe.

It is perhaps worth stressing the distinction between unpredictability and intractability. Unpredictability has nothing to do with the available computational resources. Classical systems are unpredictable (or would be, if they existed) because of their sensitivity to initial conditions. Quantum systems do not have that sensitivity, but are unpredictable because they behave differently in different universes, and so appear random in most universes. In neither case will any amount of computation lessen the unpredictability. Intractability, by contrast, is a computational-resource issue. It refers to a situation where we could readily make the prediction if only we could perform the required computation, but we cannot do so because the resources required are impractically large. In order to disentangle the problems of unpredictability from those of intractability in quantum mechanics, we have to consider quantum systems that are, in principle, predictable.

It might seem natural to conclude that reality does not, after all, display genuine computational universality, because interference phenomena cannot be usefully rendered. Feynman, however, correctly drew the opposite conclusion! Instead of regarding the intractability of the task of rendering quantum phenomena as an obstacle, Feynman regarded it as an opportunity. If it requires so much computation to work out what will happen in an interference experiment, then the very act of setting up such an experiment and measuring its outcome is tantamount to performing a complex computation. Thus, Feynman reasoned, it might after all be possible to render quantum environments efficiently, provided the computer were allowed to perform experiments on a real quantum-mechanical object.

Evidently there are computational tasks that are ‘intractable’ if we attempt to perform them using any existing computer, but which would be tractable if we were to use quantum-mechanical objects as special-purpose computers. (Notice that the fact that quantum phenomena can be used to perform computations in this way depends on their not being subject to chaos. If the outcome of computations were an inordinately sensitive function of the initial state, ‘programming’ the device by setting it in a suitable initial state would be an impossibly difficult task.)